The U.S. military intervention in Libya seems to have turned national security politics upside down in Washington.

As top Pentagon brass head to Capitol Hill again Thursday to explain things to Congress, President Barack Obama, once cast as the Nobel Peace Prize-winning liberal who tried to keep America’s military engagements at arm’s length, is now acting more like former President George H.W. Bush in the first Persian Gulf War, relying on a broad international coalition to launch a military campaign.

Some congressional Republicans who in the past have been strong defense advocates have become dovish skeptics of the Libyan intervention. And after weeks of arguing against major cuts in defense spending, they now fault the administration for the mounting costs of the airstrikes and other operations in Libya.

No one knows for sure what the ultimate outcome will be, in part because Obama is on the verge of pulling off a singular accomplishment in U.S. military history: using American military power to start a war, then dialing back to become more of an equal partner with international allies.

The script itself appears backward.

“I’ve had a number of people ask me if there is any kind of an exit strategy, although those same people didn’t ask that question about Iraq or Afghanistan, but they are asking it right now,” Sen. Ben Nelson (D-Neb.) said Tuesday.

The lack of an exit strategy, once a weapon Democrats used on former President George W. Bush and the war in Iraq, has now entered the arsenal of conservatives leery of the Libyan intervention. What’s more, some of the voices that supported intervention in Iraq are questioning why liberals were silent then but are supportive now.

“How can the left call for the ouster of Muammar Qadhafi for the sin of killing hundreds of Libyans when it opposed the war waged against Saddam Hussein?” former Florida Rep. Joe Scarborough asked Tuesday in a POLITICO column. “If Obama and his liberal supporters believed Qadhafi’s actions morally justified the Libyan invasion, why did they sit silently by for 20 years while Saddam killed hundreds of thousands?”

But even the usual partisan battle lines aren’t quite clear on Libya. Few critics have said they outright oppose Obama’s decision to stop Qadhafi’s attack on the city of Benghazi, where anti-government forces were holed up against ground units of the Libyan army.

At a Senate Armed Services Committee hearing Tuesday, Sen. John Cornyn (R-Texas) acknowledged that even as he “struggled to understand” the long-term plan for Libya, “we intervened to save civilians, which I understand, and any human being with a heart would feel compassion for.”

House Armed Services Committee Chairman Buck McKeon (R-Calif.) said before the allied airstrikes that the president “was doing a great job doing nothing.” But he conceded in a statement Tuesday that Obama acted for a “noble cause” in Libya.

The flip side is that the president doesn’t have the same kind of support from congressional allies that he could have once expected. Democrats have echoed that they’re pleased Benghazi was saved. But they, too, are uncertain of the ultimate outcome in Libya.

That’s in part because of another novel aspect of the way the Obama administration has faced the Libya challenge: Despite the hard lessons of Iraq and Afghanistan, it apparently did not begin the operation in Libya with an endgame in mind. Instead, the administration’s only initial goals were to save Benghazi and other rebel-held cities in eastern Libya and then to transfer as much responsibility as possible to an international coalition, under the assumption that it, with the U.S. in a diminished role, would determine what would come next.

Still, Obama made clear that he had some lessons from Iraq in mind in his unequivocal opposition to fielding American ground troops in Libya. To satisfy that objective, the Defense Department has been waging a campaign in Libya as operationally unusual as the political situation in the U.S.

Despite the initial perception that American and international warplanes would function as a kind of ad hoc air force for the Libyan rebels, U.S. and allied military commanders stress that’s not their job. Moreover, military officials say they have no military-to-military relationship with Libyan opposition forces, so even if the rebels wanted to appeal for help in their specific attacks on Qadhafi’s forces, they would have no way to do so.

Contrast that with repeated statements by Secretary of State Hillary Clinton that U.S. diplomats are “reaching out” to the Libyan opposition and her face-to-face meeting Tuesday with a Libyan delegation in London.

The White House, though, has chosen to keep separate these two sides of its effort on Libya, even though the State Department and the Pentagon have endured years of painful lessons about the need to cooperate in Iraq and Afghanistan.

The novelty of the Libya situation even extends to the way American forces are carrying out day-to-day operations. On Monday, an Air Force A-10 Thunderbolt II attack jet, built to destroy Soviet-era tanks in Europe, hit two Libyan boats off the coast of Misrata, sinking one of them.

It could be the first time such a warplane has taken out a naval target — again, an upside-down situation unlikely to have been envisioned by its designers.